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Appendix: II.

Four examples are given in Fig. 813, where for two spans we
merely have a duplicate of Fig. 401, p. 443. In all cases the
parabolas W / -v- 8 are first drawn for free beams, and these are
next opposed by a curve of reactionary moments, consisting of
straight lines shewing zero at the extreme ends. In the figure the
actual moments are drawn and stated, as found from Clapeyron's
formula, the shaded curve giving the final Bm; but the second or

opposing curve may be very closely obtained in a graphic manner.
Divide every span in thirds, drawing vertical lines, and on every
vertical except the outside ones put a mark at f of W/~ 8. Then
pass the second curve through these points so as to give the best
average results, which is easiest done by string, pins, and weights,
as at A. This method, which is due to. Claxton Fidler, is clearly
an extension of the principles already explained, and has the
advantage of being applicable to any mode of fairly uniform load-
ing, however much it may vary from span to span. (See p. 953.)